Velocity of water from tap to fill a cracked bucket to brim Let us consider a real life situation.
The bucket in figure below (drawn using MS PAINT)  has an irregular crack of essentially small area. And I decide to open a tap above it and start filling it with water.

Say, the crack starts at a distance $x\,\mathrm{cm.}$ from bottom surface and ends about $y\,\mathrm{cm.}$ from below. The area covered by crack is $q\,\mathrm{sq.cm.}$
My questions are:


*

*Is there any constant speed, to which if the flow of water from tap be set, the  water level in bucket will reach the brim irrespective of water continuing to flow out through crack? 

*If such speed exists, does it depend on shape of crack?

*If such speed does not exist, is there any other way to control and vary only the speed of water flow and fill water to brim?

*Finally, what happens if the speed of flow of water tends to c(speed of light)?


P.S. If possible, consider flow of water to be turbulent. That is what I meant by real life situation. Again IF POSSIBLE ONLY.
 A: You certainly can accomplish what you want. Whether you can calculate it with sufficient accuracy is largely a function of need, and access to CFD codes and resources.  
The shape of the crack certainly has a reasonable influence on what you want to engineer. You cannot reasonably consider the fluid inside the bucket to be a purely turbulent regime. The shape of the crack, the head pressure above it, and the characteristics of the in-flow of fluid will all impact whether any laminar flow characteristics can form in the outlet through the crack. 
If a 'purely' laminar flow were to form, then you could presume a constancy in outflow.  The same expectation would occur in a 'purely' turbulence regime. You will be in the middle, which will lead to some nonlinearity in the outflow.  Easiest way to determine this is through experimentation. From experience, oscillation from the inflow (splashing, etc) will create the biggest nonlinearity... Unless the bucket is also vibrating. 
If you must model the outflow, seek to break-down the crack into sections that have more-well-defined characteristics as a 'nozzle'. The 'edges' on which they 'join' will be more laminar and change the rest of the transfer. 

I'm going to leave out this bit about approach C. The mechanics of your gedanken do not translate to relativistic system (in any way that is apparent in your question) 
